Here's a half-baked idea:
A dedicated atmega1280 40 pin dip to drive your displays. Enough pins for 16 cathodes and 9 anodes (with 9 pnp transistors attached). It could communicate to your other Ardino via i2c or serial.
Current limits of the chip might be the problem. It has 2 ground pins and 2 Vcc pins, although one is supposed to be for Analog, so not sure whether that means a total max current of 200mA or perhaps 400mA?
If it is 400mA, that should be enough to sink 20mA from each of 16 cathodes, as long as you can spread the current over the various groups of pins which have 150mA or 100mA limits. Combined with a 1:9 multiplex ratio, it might be bright enough.
Need someone familliar with the 1280's data sheet to confirm this. Bob?
Failing that you would be looking at another 16 npns...
Paul